{"paper":{"title":"An exponential kernel associated with operators that have one-dimensional self-commutators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.FA","authors_text":"Kevin F. Clancey","submitted_at":"2018-08-28T18:44:54Z","abstract_excerpt":"The exponential kernel \\[E{g}(\\lambda,w) = \\exp -\\frac{1}{\\pi}\\int_{\\mathbb{C} } \\frac{g(u)}{\\overline{u-w} (u-\\lambda) } da(u ),\\] where the compactly supported bounded measurable function $g$ satisfies $0 \\leq g\\leq 1,$ and suitably defined for all complex $\\lambda, w,$ plays a role in the theory of Hilbert space operators with one-dimensional self-commutators and in the theory of quadrature domains. This article studies continuity and integral representation properties of $E_{g}$ with further applications of this exponential kernel to operators with one-dimensional self-commutator."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.09487","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}